envfit {vegan} | R Documentation |
The function fits environmental vectors or factors onto an ordination. The projections of points onto vectors have maximum correlation with corresponding environmental variables, and the factors show the averages of factor levels.
## Default S3 method: envfit(X, P, permutations = 0, strata, choices=c(1,2), ...) ## S3 method for class 'formula': envfit(formula, data, ...) ## S3 method for class 'envfit': plot(x, choices = c(1,2), arrow.mul, at = c(0,0), axis = FALSE, p.max = NULL, col = "blue", add = TRUE, ...) ## S3 method for class 'envfit': scores(x, display, choices, ...) vectorfit(X, P, permutations = 0, strata, choices=c(1,2), display = c("sites", "lc"), w = weights(X), ...) factorfit(X, P, permutations = 0, strata, choices=c(1,2), display = c("sites", "lc"), w = weights(X), ...)
X |
Ordination configuration. |
P |
Matrix or vector of environmental variable(s). |
permutations |
Number of permutations for assessing significance of vectors or factors. |
formula, data |
Model formula and data. |
x |
A result object from envfit . |
choices |
Axes to plotted. |
arrow.mul |
Multiplier for vector lengths. The arrows are
automatically scaled similarly as in plot.cca if this
is not given and add = TRUE . |
at |
The origin of fitted arrows in the plot. If you plot arrows
in other places then origin, you probably have to specify
arrrow.mul . |
axis |
Plot axis showing the scaling of fitted arrows. |
p.max |
Maximum estimated P value for displayed
variables. You must calculate P values with setting
permutations to use this option. |
col |
Colour in plotting. |
add |
Results added to an existing ordination plot. |
strata |
An integer vector or factor specifying the strata for permutation. If supplied, observations are permuted only within the specified strata. |
display |
In fitting functions these are ordinary site scores or
linear combination scores
("lc" ) in constrained ordination (cca ,
rda , capscale ). In scores
function they are either "vectors" or "factors"
(with synonyms "bp" or "cn" , resp.). |
w |
Weights used in fitting (concerns mainly cca
and decorana results which have nonconstant weights). |
... |
Parameters passed to scores . |
Function envfit
finds vectors or factor averages of
environmental variables. Function plot.envfit
adds these in an
ordination diagram. If X
is a data.frame
,
envfit
uses factorfit
for factor
variables and
vectorfit
for other variables. If X
is a matrix or a
vector, envfit
uses only vectorfit
. Alternatively, the
model can be defined a simplified model formula
, where
the left hand side must be an ordination result object or a matrix of
ordination scores, and right hand
side lists the environmental variables. The formula interface can be
used for easier selection and/or transformation of environmental
variables. Only the main effects will be analysed even if interaction
terms were defined in the formula.
Functions vectorfit
and factorfit
can be called directly.
Function vectorfit
finds directions in the ordination space
towards which the environmental vectors change most rapidly and to
which they have maximal correlations with the ordination
configuration. Function factorfit
finds averages of ordination
scores for factor levels. Function factorfit
treats ordered
and unordered factors similarly.
If permutations
> 0, the `significance' of fitted vectors
or factors is assessed using permutation of environmental variables.
The goodness of fit statistic is squared correlation coefficient
(r^2).
For factors this is defined as r^2 = 1 - ss_w/ss_t, where
ss_w and ss_t are within-group and total sums of squares.
User can supply a vector of prior weights w
. If the ordination
object has weights, these will be used. In practise this means that
the row totals are used as weights with
cca
or decorana
results. If you do not
like this, but want to give
equal weights to all sites, you should set w = NULL
.
The weighted fitting gives similar results to biplot
arrows and class centroids in cca
.
For complete
similarity between fitted vectors and biplot arrows, you should set
display = "lc"
(and possibly scaling = 2
).
The lengths of arrows for fitted vectors are automatically adjusted
for the physical size of the plot, and the arrow lengths cannot be
compared across plots. For similar scaling of arrows, you must
explicitly set the arrow.mul
argument in the plot
command.
The results can be accessed with scores.envfit
function which
returns either the fitted vectors scaled by correlation coefficient or
the centroids of the fitted environmental variables.
Functions vectorfit
and factorfit
return lists of
classes vectorfit
and factorfit
which have a
print
method. The result object have the following items:
arrows |
Arrow endpoints from vectorfit . The arrows are
scaled to unit length. |
centroids |
Class centroids from factorfit . |
r |
Goodness of fit statistic: Squared correlation coefficient |
permutations |
Number of permutations. |
pvals |
Empirical P-values for each variable. |
Function envfit
returns a list of class envfit
with
results of vectorfit
and envfit
as items.
Function plot.envfit
scales the vectors by correlation.
Fitted vectors have become the method of choice in displaying
environmental variables in ordination. Indeed, they are the optimal
way of presenting environmental variables in Constrained
Correspondence Analysis cca
, since there they are the
linear constraints.
In unconstrained ordination the relation between external variables
and ordination configuration may be less linear, and therefore other
methods than arrows may be more useful. The simplest is to adjust the
plotting symbol sizes (cex
, symbols
) by
environmental variables.
Fancier methods involve smoothing and regression methods that
abound in R, and ordisurf
provides a wrapper for some.
Jari Oksanen. The permutation test derives from the code suggested by Michael Scroggie.
A better alternative to vectors may be ordisurf
.
data(varespec) data(varechem) library(MASS) ord <- metaMDS(varespec) (fit <- envfit(ord, varechem, perm = 999)) scores(fit, "vectors") plot(ord) plot(fit) plot(fit, p.max = 0.05, col = "red") ## Adding fitted arrows to CCA. We use "lc" scores, and hope ## that arrows are scaled similarly in cca and envfit plots ord <- cca(varespec ~ Al + P + K, varechem) plot(ord, type="p") fit <- envfit(ord, varechem, perm = 999, display = "lc") plot(fit, p.max = 0.05, col = "red") ## Class variables, formula interface, and displaying the ## inter-class variability with `ordispider' data(dune) data(dune.env) attach(dune.env) ord <- cca(dune) fit <- envfit(ord ~ Moisture + A1, dune.env) plot(ord, type = "n") ordispider(ord, Moisture, col="skyblue") points(ord, display = "sites", col = as.numeric(Moisture), pch=16) plot(fit, cex=1.2, axis=TRUE)